There's a lot of middle ground between getting as dirty as the PC's currently do, and never getting dirty at all.
Like getting a little bit of blood and dirt on your clothes or armor in combat, but not all over your face. A face would be easy to wipe clean anyway so the face dirt shouldn't last long.
That or give us an option to shower at camp before we go to sleep, or add a cantrip called: delousing. You can make an additional simple add on- if your covered in dirt or blood, you get a -3 to persuasion and stealth as you look homeless and smell so bad, that enemies can detect your stink
